Jacques Bros

Towards a relativistic KMS-condition

Abstract It is shown that, under quite general conditions, thermal correlation functions in relativistic quantum field theory have stronger analyticity properties in configuration space than those imposed by the KMS-condition. These analyticity properties may be understood as a remnant of the relativistic spectrum condition in the vacuum sector and lead to a Lorentz-covariant formulation of the KMS-condition involving all space-time variables.

The lifetime of a massive particle in a de Sitter universe

We study particle decay in de Sitter spacetime as given by first-order perturbation theory in an interacting quantum field theory. We show that for fields with masses above a critical mass mc there is no such thing as particle stability, so that decays forbidden in flat spacetime do occur there. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with the de Sitter radius. Particles with lower mass are even stranger: the masses of their decay products must obey quantification rules, and their lifetime is zero.

Particle Decays and Stability on the de Sitter Universe

We study particle decay in de Sitter space–time as given by first-order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the “phase space” coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass mc there is no such thing as particle stability, so that decays forbidden in flat space–time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero.

Triangular Invariants, Three-Point Functions and Particle Stability on the de Sitter Universe

We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle identity living on the cone and on the complex de Sitter manifold. We discuss an application of the general results to the study of the stability of scalar particles on the de Sitter universe.

Towards a General Theory of Quantized Fields on the Anti-de Sitter Space-Time

Abstract: We propose a general framework for studying quantum field theory on the anti-de-Sitter space-time, based on the assumption of positivity of the spectrum of the possible energy operators. In this framework we show that the n-point functions are analytic in suitable domains of the complex AdS manifold, that it is possible to Wick rotate to the Euclidean manifold and come back, and that it is meaningful to restrict AdS quantum fields to Poincaré branes. We give also a complete characterization of two-point functions which are the simplest example of our theory. Finally we prove the existence of the AdS-Unruh effect for uniformly accelerated observers on trajectories crossing the boundary of AdS at infinity, while that effect does not exist for all the other uniformly accelerated trajectories.

A general construction of conformal field theories from scalar anti-de Sitter quantum field theories

We provide a new general setting for scalar interacting fields on the covering of a ( d+1 )-dimensional AdS spacetime. The formalism is used at first to construct a one-parameter family of field theories, each living on a corresponding spacetime submanifold of AdS, which is a cylinder R×Sd−1 . We then introduce a limiting procedure which directly produces Luscher–Mack CFTs on the covering of the AdS asymptotic cone. Our generalized AdS → CFT construction is nonperturbative, and is illustrated by a complete treatment of two-point functions, the case of Klein–Gordon fields appearing as particularly simple in our context. We also show how the Minkowskian representation of these boundary CFTs can be directly generated by an alternative limiting procedure involving Minkowskian theories in horocyclic sections (nowadays called ( d− 1)-branes, 3-branes for AdS5 ). These theories are restrictions to the brane of the ambient AdS field theory considered. This provides a more general correspondence between the AdS field theory and a Poincare invariant QFT on the brane, satisfying all the Wightman axioms. The case of two-point functions is again studied in detail from this viewpoint as well as the CFT limit on the boundary.

Braid Group Statistics Implies Scattering in Three-Dimensional Local Quantum Physics

AbstractIt is shown that quantum fields for massive particles with braid group statistics (Plektons) in three-dimensional space-time cannot be free, in a quite elementary sense: They must exhibit elastic two-particle scattering into every solid angle, and at every energy. This also implies that for such particles there cannot be any operators localized in wedge regions which create only single particle states from the vacuum and which are well-behaved under the space-time translations (so-called temperate polarization- free generators). These results considerably strengthen an earlier “NoGo-theorem for ’free’ relativistic Anyons”.As a by-product we extend a fact which is well-known in quantum field theory to the case of topological charges (i.e., charges localized in space-like cones) in d ≥ 4, namely: If there is no elastic two-particle scattering into some arbitrarily small open solid angle element, then the 2-particle S-matrix is trivial.

Asymptotic dynamics of thermal quantum fields

Abstract It is shown that the timelike asymptotic properties of thermal correlation functions in relativistic quantum field theory can be described in terms of free fields carrying some stochastic degree of freedom which couples to the thermal background. These “asymptotic thermal fields” have specific algebraic properties (commutation relations) and their dynamics can be expressed in terms of asymptotic field equations. The formalism is applied to interacting theories where it yields concrete non-perturbative results for the asymptotic thermal propagators. The results are consistent with the expected features of dissipative propagation of the constituents of thermal states, outlined in previous work, and they shed new light on the non-perturbative effects of thermal backgrounds.

Microcausality and energy positivity in all frames imply Lorentz invariance of dispersion laws

A new presentation of the Borchers-Buchholz result of the Lorentz-invariance of the energy-momentum spectrum in theories with broken Lorentz symmetry is given in terms of properties of the Greens functions of microcausal Bose and Fermi-fields. Strong constraints based on complex geometry phenomenons are shown to result from the interplay of the basic principles of causality and stability in Quantum Field Theory: if microcausality and energy-positivity in all Lorentz frames are satisfied, then it is unavoidable that all stable particles of the theory be governed by Lorentz-invariant dispersion laws: in all the field sectors, discrete parts outside the continuum as well as the thresholds of the continuous parts of the energy-momentum spectrum, with possible holes inside it, are necessarily represented by mass-shell hyperboloids (or the light-cone). No violation of this geometrical fact can be produced by spontaneous breaking of the Lorentz symmetry.

Particles and propagators in relativistic thermo field theory

Based on a new spectral representation of thermal correlation functions, a general characterization of stable particles in relativistic thermo field theory is given. Such particles manifest themselves by specific discrete contributions in the spectral functions and can thus be identified unambiguously.